# Work done by tension

1. Jan 27, 2007

### dnt

1. The problem statement, all variables and given/known data

A simple pendulum, consisting of mass m and a string, swings upward making an angle X with the vertical. What is the work done by the tension force? (answer in terms of mg)

2. Relevant equations

W=Fd

3. The attempt at a solution

What I need to do is solve for the tension force, which at the bottom of the pendulum is simply mg, right? However I am having trouble determing the distance that the tension force is applied to. Can anyone get me started in the right direction? Thanks.

2. Jan 27, 2007

### robphy

Is W=Fd? What does each term mean?

3. Jan 27, 2007

### turdferguson

The tension doesnt equal weight at the bottom, its going in a circle. My guess would be to use the work energy theorem, but the question is pretty vague and the magnitude of tension changes at each point in the swing

4. Jan 28, 2007

### Gib Z

W only equals Fs if the vectors are both in the same direction.

You want the dot product of the Vectors Force and displacement.

That is given for vectors v and w by $$v^{\rightarrow} \cdot w^{\rightarrow} = ||v^{\rightarrow}|| ||w^{\rightarrow}|| \cos \theta$$ Where $$||v^{\rightarrow}||$$ is the magnitude of vector v. Same would apply to w. Theta is the angle between the two vectors.

So for work we will have two vectors given, the Force and displacement. Since we only want the force vector in the same direction as the displacement, we break it into 2 components, Force Parallel to displacement, and Force Perpendicular to Displacement.

Draw a simple right angle triangle with F vector as the hypotenuse, and draw the other 2 sides as the components, Parallel and Perpendicular. It is easy to see from the diagram that the Parallel vector is given by the F vector multiplyed by cos theta, and Perpendicular Vector by sin theta.

This ties in with common sense, because If the angle is zero, then there is no perpendicular force, and Fsin theta shows that. And the parallel force is the only force is the angle is zero, also shown by the formula.

Using those, you can find out the Magnitude of the Parallel vector, which is Fcos theta, multiply it by s and we get the work done :).

Sorry if alot of this was old knowledge, i did it just incase you didnt know.

5. Jan 28, 2007

### P3X-018

It's not just "multiply it by s" Gib Z, since the force varies with angle theta, he needs to integrate your given force from maximum deflection angle to 0. Use that $\mathrm{d}s = L\mathrm{d}\theta$, where $L$ is the length of the string holding the pendulum.

Last edited: Jan 28, 2007
6. Jan 28, 2007

### Gib Z

>.< Your Right of course, I must learn to read the question lol. I just read robphys post, because usually the 2nd post gives what the original poster did wrong away...>.< my bad

7. Jan 28, 2007

### PhanthomJay

You should note that the tension force is always perpendicular to the displacement of the bob. Using the definitionn of work, what does that tell you about the work done by the tension force?